Here are the graphs of the functions:

1. $f(x) = 3^x$ (solid line): This graph shows exponential growth as $x$ increases. The function grows rapidly for positive $x$-values and approaches zero for negative $x$-values but never reaches it.

2. $g(x) = \left(\frac{1}{3}\right)^x$ (dashed line): This graph represents exponential decay. As $x$ increases, $g(x)$ approaches zero, while for negative $x$-values, it increases towards infinity.

These graphs illustrate the contrasting behavior of exponential growth and decay based on the base of the exponent.

Would you like to explore further details or have any questions?

Related Questions:

1. How do transformations affect the graphs of exponential functions?
2. What are the asymptotic properties of $f(x) = 3^x$ and $g(x) = \left(\frac{1}{3}\right)^x$?
3. Can exponential functions ever cross the x-axis or y-axis?
4. How does the rate of growth or decay differ between different bases in exponential functions?
5. What real-world phenomena could these exponential growth and decay models represent?

Tip:

When graphing exponential functions, remember that their general form, $y = a^x$, will approach zero for large negative $x$-values if $a > 1$ and approach infinity if $0 < a < 1$.